If the airline would have been say, CX connecting to a UA flight and different tickets were issued, you would be assured that CX would be responsible for getting you to connect even on seperate tickets.. but then, that's CX and not UA!

Ok... the main problems here are:

1. You are a in a group of 20 people.
2. You should have checked in as a group and not individually.
3. Your agent should have booked all of you as ONE group instead of just issuing seperate PNRs for everyone.
4. Your agent should have blocked booked everyone one one airline preferbly.. even if it means codesharing... ie your domestic flights as NH flight numbers.

But knowing how Thailand agents work.. that is not possible on most fares ex-BKK. And the agent would have split the booking up into 2 seperate tickets, as codeshare is just a word and not actively used in asia. But then, it would have been the agents' responsibility to have documented and advised UA that this group is connecting to the NH flight with UA directly so that anything of this sort (cancellations) would have protected your group onto the fastest and best connection to LAX.